In this article we will learn how to simplify exponents.

### Simplifying rational exponents

The base b raised to the power of n/m is equal to:

*b ^{n/m} = (^{m}√b)^{n} = ^{m}√(b^{n})*

For example:

2^{3/2} = ^{2}√(2^{3}) = 2.828

### Simplifying fractions with exponents

Fractions with exponents:

*(a / b) ^{n} = a^{n} / b^{n}*

For example:

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(4/3)^{3} = 4^{3 }/ 3^{3} = 64 / 27 = 2.37

### Simplifying negative exponents

The base b raised to the power of minus n is equal to 1 divided by the base b raised to the power of n:

*b ^{-n} = 1 / b^{n}*

For example:

2^{-3} = 1/2^{3} = 1/(2⋅2⋅2) = 1/8 = 0.125

### Simplifying radicals with exponents

For radical with exponent:

*( ^{m}√a)^{n} = a^{n/m}*

For example:

(√5)^{4} = 5^{4/2} = 5^{2} = 25

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